In this paper, the well-known proportional hazards model which includes several well-known lifetime distributions such as exponential,Pareto, Lomax, Burr type XII, and so on is considered. With both Bayesian and non-Bayesian approaches , we consider the estimation of parameters of interest based on progressively Type-II right censored samples. The Bayes estimates are obtained based on symmetric and asymmetric loss functions. We also provide Bayes and empirical Bayes prediction intervals for the times to failure of units censored in multiple stages in a progressively censored sample. Finally, two numerical examples are given to illustrate the results.